Abstract : Maximum entropy models (MEM) have been widely used in the last 10 years for
modelling, explaining and predicting the statistics of networks of spiking neurons.
However, as the network size increases, the number of model parameters increases
rapidily, hindering its interpretation and fast computation. However, these parameters
are not necessarily independent from each other; when some of them are related by
hidden dependencies, their number can be reduced, allowing to map the MEM into a
lower dimensional space. Here, we present a novel framework for MEM dimensionality
reduction that uses the geometrical properties of MEM to find the subset of dimensions
that best captures the network high-order statistics, without fitting the model to data.
This allows us define a parameter somehow representing the degree of compressibility of
the code. The method was tested on synthetic data where the underlying statistics is
known and on retinal ganglion cells (RGC) data recorded using multi-electrode arrays
(MEA) under different stimuli. We found that MEM dimensionality reduction depends
on the interdependences between the network activity, the density of the raster and the
number of observed events. For RGC data we found that the activity is highly
interdependent, with a dimensionality reduction of almost 50%, compared to a random
raster, showing that the network activity is highly compressible, possibly due to the
network redundancies. This dimensionality reduction depends on the stimuli statistics,
supporting the idea that sensory networks adapts to stimuli statistics, modifying the
level of redundancy, i.e. the coding strategy.